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Abstract
We derive the tail distribution of the workloads for each server and the approximation for the tail sojourn times based on large deviation analysis. Furthermore, we optimize the cluster sizes that fulfill the requirements of target tail sojourn times. Extensive simulation experiments show very good matches to the derived analysis in a variety of scenarios, i.e., large numbers of servers experiencing a high number of different execution speeds, under various traffic intensities, workload variations and cluster sizes. Finally, we apply our proposed analysis on estimating the tail sojourn times of a Wikipedia system hosted in a private cloud, and the tested results strongly confirm the applicability and accuracy of our analysis. Our research here aims to address the challenging question of how to best dimension the size of a cluster deployed in a cloud, in terms of number of VMs experiencing varying execution speeds, so that the target value of tail sojourn times can be met. We particularly take an analytical perspective and focus on deriving the tail response times for any given cloud cluster size using various key system parameters.